Question

Assume that the air you exhale is at 35°C, with a relative humidity of 90%. This air immediately mixes with environmental air at 5°C and unknown relative humidity; during the mixing, a variety of intermediate temperatures and water vapour percentages temporarily occur. If you are able to "see your breath" due to the formation of cloud droplets during this mixing, what can you conclude about the relative humidity of your environment? (Refer to the vapour pressure graph drawn in Problem 5.42.)

Short answer

The relative humidity required to produce cloud droplets is around 25%.

Step-by-step solution

Given information

Consider the initial water vapour pressure of air mixed at temperatures of 10°C and 35°C. When the air particles have the same mass, the air mixture should have a half-temperature of between 10 and 35 degrees Celsius.

The reason for this is that air's heat capacity is independent of its temperature. In the same way, the water partial pressure is half way between the air particle starting pressures. The air mixture temperature and water partial pressure lie on the straight line in the figure for any value of the initial mass ratio.

Explanation

Use the vapour pressure graph from problem 5.42 to graph the compositions of exhaled air at 35° and 90% relative humidity, as well as the composition of outside air, as illustrated in the diagram below.

P is the partial pressure of water in bar, and T is the temperature in degrees Celsius. In the diagram above, the lower dot represents the external air temperature (10°C) and the top dot represents the exhaled air temperature (35°C).

Conclusion

Cloud droplets are formed when the state of the mixture is above the equilibrium curve, as indicated in the diagram. Because both initial states are below the curve, this is conceivable.

When the outdoor air dot goes vertically downward, the vapour pressure curve may be crossed. The minimal partial pressure in this situation is 0.003 bar, while the relative humidity is around 25%, according to the graph.

As a result, the relative humidity required to produce cloud droplets is around 25%.